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Colloquium - 19 Oct 2000

Department of Statistics
Texas A&M University

ABSTRACT: Formal Bayesian comparison of models is typically done using Bayes factors which are ratios of model marginal likelihoods. In general, the model marginal likelihood is not straightforward to estimate which has hindered the routine use of Bayes factors in practice. Over the last several years a number of methods have emerged that utilize the output of Markov chain Monte Carlo simulations to find the marginal likelihood. In this talk we discuss one particular method, that due to Chib (1995), which is simpler than other methods. This method exploits specific features of the MCMC simulation scheme to produce an estimate of the marginal likelihood. In the first part of the talk we present an extension of this method that can be applied to MCMC chains arising from the single or multiple-block Metropolis-Hastings algorithm. This extension considerably broadens the applicability of the method. In the second part of the talk we discuss how the same method can be used to find the marginal likelihood of Dirichlet process mixture models, thus leading to an approach for comparing semi-parametric and parametric Bayesian models. A number of examples are used to illustrate the ideas.

Refreshments will be served in the Blocker Building, Room 447, at 3:30 p.m.

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